1. Field of the Invention
The present invention relates to a filter circuit and, more particularly, to a filter circuit with an automatic regulating function which is adapted to provide a constant input-output characteristic independent of variations in values of elements when fabricated.
2. Description of the Background Art
Elements of the same type formed in one semiconductor integrated circuit are characterized by a substantially constant variation tendency of their characteristic values such as resistances and capacitances when fabricated. A circuit arrangement making use of this property can prevent the variations in element characteristic values in the circuit from being reflected upon variations in circuit characteristics.
The absolute values of the element characteristic values sometimes vary when the elements are fabricated, and there is no correlation between variation tendencies of different types of elements. For example, in a filter circuit whose characteristics are determined by a resistance and a capacitance, the variations in values of elements when fabricated result in variations in characteristics of the filter circuit itself.
FIG. 8 is a circuit diagram of an example of conventional integrated filter circuits. As shown in FIG. 8, the filter circuit comprises a filter portion 8 and a control portion 9. FIG. 9 is a circuit diagram schematically showing the internal construction of the filter portion 8.
Referring to FIG. 9, the filter portion 8 includes a voltage-controlled current source 13 having a mutual conductance gm, a capacitor C.sub.1, and a buffer 14. The filter portion 8 receives an input signal v.sub.in given from an input signal source 51 through an input terminal 1 and filters the input signal v.sub.in on the basis of RC characteristics set therein to output an output signal v.sub.out at an output terminal 2.
The voltage-controlled current source 13 includes PNP bipolar transistors T1, T2, NPN bipolar transistors T10 to T15, and reference current sources 81, 82 for supplying a reference current I.sub.1, as shown in FIG. 8. The transistors T10 and T11 form a differential pair. The input signal v.sub.in is applied to the base of the transistor T10, and the output terminal 2 is connected to the base of the transistor T11. The emitter of the transistor T10 is grounded through the reference current source 81, and the emitter of the transistor T11 is grounded through the reference current source 82. A resistor R.sub.1 is connected between the emitters of the transistors T10 and T11. The reference current sources 81, 82 specify the sum of the amounts of current flowing in the transistors T10 and T11.
The transistors T1, T2, T12 to T15 form a load current control portion. The transistors T1, T12, T13 control the collector current of the transistor T10, and the transistors T2, T14, T15 control the collector current of the transistor T11. The transistors T1 and T2 form a current mirror circuit. The transistors T1 and T2 are of the same transistor size, the transistors T12 to T15 are of the same transistor size, and the transistors T10 and T11 are of the same transistor size.
The voltage-controlled current source 13 as above constructed includes a differential amplifier circuit having the differential pair of transistors T10 and T11, the base input of the transistor T10 serving as a positive input of the voltage-controlled current source 13, the base input of the transistor T11 serving as a negative input thereof, the collector of the transistor T15 at a node N1 serving as the output thereof. The voltage-controlled current source 13 supplies an output current I.sub.16 at its output on the basis of a potential difference between the positive and negative inputs thereof. The capacitor C.sub.1 is connected between the node N1 which is the output of the voltage-controlled current source 13 and ground.
The buffer 14 includes an NPN bipolar transistor T3, a diode D1 and a reference current source 83 connected in series between a power supply V.sub.cc and ground, as shown in FIG. 8. The base of the transistor T3 is connected to the output node N1 of the voltage-controlled current source 13 and a first electrode of the capacitor C.sub.1. A voltage given from the cathode of the diode D1 at a node N2 serves as the output voltage v.sub.out, which is outputted at the output terminal 2 and is applied to the base input of the transistor T11.
That is, the filter portion 8 is of a negative feedback arrangement which receives the input signal v.sub.in at positive input and receives the output voltage v.sub.out of the buffer 14 at negative input.
The control portion 9 includes NPN bipolar transistors T17 to T20, a reference voltage source 91 for generating a reference voltage V.sub.1, and reference current sources 92, 93 for supplying a reference current I.sub.2.
The transistors T19 and T20 form a differential pair. The reference voltage V.sub.1 is applied to the base of the transistor T19 from the reference voltage source 91, and a reference control voltage V.sub.2 is applied to the base of the transistor T20 from an exterior reference voltage source 90 through a terminal 3.
The transistors T17, T18 have bases commonly receiving a predetermined reference voltage from a reference voltage source 94, collectors connected commonly to the power supply V.sub.cc, and emitters connected to the collectors of the transistors T19, T20, respectively, and serve as a load current control portion.
The emitter of the transistor T19 is grounded through the reference current source 92, and the emitter of the transistor T20 is grounded through the reference current source 93. A resistor R.sub.2 is connected between the emitters of the transistors T19 and T20. The reference current sources 92 and 93 control the sum of the amounts of current flowing in the transistors T19 and T20.
The collector of the transistor T19 at a node N11 is connected to the bases of the transistors T12 and T14 of the voltage-controlled current source 13, and the collector of the transistor T20 at a node N12 is connected to the bases of the transistors T13 and T15 of the voltage-controlled current source 13.
The input-output characteristic of the filter circuit of FIGS. 8 and 9 is basically determined by the resistance and capacitance of the resistor R.sub.1 and capacitor C.sub.1 in the voltage-controlled current source 13 and may be changed by the control circuit 9. The characteristic of the filter circuit will now be derived with reference to FIG. 9. EQU I=gm(V.sub.in -V.sub.out) (1)
where gm is a mutual conductance of the voltage-controlled current source 13, I is the value of the output current I.sub.16 of the voltage-controlled current source 13, C is the capacitance of the capacitor C.sub.1, V.sub.in is the signal level of the input signal v.sub.in, and V.sub.out is the level of the output voltage v.sub.out. ##EQU1##
Then, I is eliminated from Expressions (1) and (2) to find the input-output characteristics of the voltage-controlled current source 13. ##EQU2## A cut-off frequency f.sub.c of the filter is determined from Expression (3). ##EQU3##
As shown in FIG. 8, the filter portion 8 is formed in such a manner that the capacitor C.sub.1 is added to the voltage-controlled current source 13 including the differential amplifier circuit. The voltage-controlled current source 13 is adapted so that the output current I.sub.16 changes in accordance with a potential difference between the input level V.sub.in of the input signal source 51 and the output level V.sub.out of the output terminal 2. The mutual conductance gm of the voltage-controlled current source 13 may be controlled by the exterior constant voltage source V.sub.2 connected to the terminal 3, as will be described below. ##EQU4## EQU I.sub.12 +I.sub.13 =I.sub.10 ( 6) EQU I.sub.14 +I.sub.15 =I.sub.11 ( 7)
where I.sub.10 to I.sub.15 are collector current values of the transistors T10 to T15, and I.sub.17 and I.sub.18 are collector current values of the transistors T17 and T18, respectively.
Changing Expressions (5) to (7) into ##EQU5## Further ##EQU6##
The following expressions hold ##EQU7## where R.sub.1 is the resistance of the resistor R.sub.1, and R.sub.2 is the resistance of the resistor R.sub.2.
Inserting Expressions (11) to (14) into Expression (10), Expression (15) holds. The mutual conductance gm is determined by Expression (16). ##EQU8##
From Expression (16), it is understood that the mutual conductance gm of the voltage-controlled current source 13 is controlled by the control voltage V.sub.2 given from the terminal 3. A cut-off frequency f.sub.8 which is the input-output characteristic of the filter circuit is determined from Expression (4) if the mutual conductance gm and the capacitance are determined. Then Expression (17) holds. ##EQU9##
It will be appreciated from Expression (17) that the input-output characteristic of the filter circuit is changed by the control voltage V.sub.2 given from the exterior. Thus, the variations in input-output characteristic of the filter circuit may be controlled by adjusting the value of the control voltage V.sub.2 if the absolute values of the elements when fabricated vary within a variable range of the filter portion 8 and the control portion 9.
However, for practical mass production of products in which such a filter circuit is mounted, it is necessary to adjust a control voltage corresponding to the control voltage V.sub.2 for each of the products, resulting in increased costs which is impractical.
To solve the problem, it has been considered to provide an automatic regulating circuit for keeping the characteristic of the circuit itself constant independent of variations in characteristic values of the elements when fabricated.
FIGS. 10A and 10B are a circuit diagram of an example of conventional filter circuits with an automatic regulating function. As shown in FIGS. 10A and 10B, the filter circuit comprises a reference signal source 4, an amplitude detector 5, an amplitude detector 6, an operational amplifier 7, a resistor R.sub.4, a resistor R.sub.5, a reference filter portion 10, and a control portion 11 as well as the filter portion 8 and the control portion 9. The filter portion 8 and the control portion 9 of FIGS. 10A and 10B are similar in construction to those of FIG. 8 except that the base input of the transistor T19 of the control portion 9 receives the output voltage V.sub.1 of the operational amplifier 7, and the description thereof will be omitted herein.
The amplitude detectors 5 and 6 have completely the same characteristic, and the operational amplifier 7 has a sufficiently large gain. A reference signal S4 generated by the reference signal source 4 uses a sine wave having constant amplitude and frequency. The reference signal S4 is applied to the reference filter portion 10 and is dammed by the resistors R.sub.4 and R.sub.5 at a predetermined rate into a damped signal S45 which is in turn applied to the amplitude detector 6.
The amplitude detector 5 receives an output signal S10 and applies an output signal S5 to a negative input of the operational amplifier 7. The amplitude detector 6 receives the damped signal S45 and applies an output signal S6 to a positive input of the operational amplifier 7. The operational amplifier 7 outputs the control voltage V.sub.1 on the basis of a potential difference between the two signals S5 and S6.
The reference filter portion 10 is equivalent in construction to the filter portion 8, and includes transistors T101 to T103 corresponding to the transistors T1 to T3, transistors T111 to T115 corresponding to the transistors T10 to T15, a reference current source 103 corresponding to the reference current source 83, and a diode D101 corresponding to the diode D1. The above-mentioned respective corresponding elements have completely the same individual size and characteristic as well as the same connection to their peripheral portions. Nodes N101 and N102 correspond to the nodes N1 and N2, respectively.
The resistor R.sub.3 corresponds to the resistor R.sub.1, and the capacitor C.sub.2 corresponds to the capacitor C.sub.1. Reference current sources 101, 102 correspond to the reference current sources 81, 82, respectively, and specify the sum of the amounts of current flowing in the transistors T111 and T111. The abovementioned respective corresponding elements have the same connection to their peripheral portions but have different individual characteristic values such as resistances, capacitances, and supply current values.
The control portion 11 is equivalent in construction to the control portion 9, and includes transistors T117 to T120 corresponding to the transistors T17 to T20, a resistor R.sub.2 corresponding to the resistor R.sub.2 (designated by the same reference character to manifest the same resistance), reference current sources 112, 113 corresponding to the reference current sources 92, 93 for specifying the sum of the amounts of current flowing in the transistors T119, T120, and a reference voltage source 104 corresponding to the reference voltage source 94. The above-mentioned respective corresponding elements have completely the same individual size and characteristic as well as the same connection to their peripheral portions. Nodes N111 and N112 correspond to the nodes N11 and N12, respectively. The control portion 11 differs from the control portion 9 only in that a constant voltage V.sub.3 is applied to the base of the transistor T120 from a reference voltage source 105.
Connection between the reference filter portion 10 and the control portion 11 is equivalent to connection between the filter portion 8 and the control portion 9 of FIG. 8 except that the output voltage V.sub.1 of the operational amplifier 7 is applied to the bases of the transistors T19 and T119 of the control portions and 11.
The resistance and capacitance of the resistor R.sub.3 and capacitor C.sub.2 of the reference filter portion 10 are selected to provide an input-output characteristic which damps the reference signal S4 to (R.sub.5 /(R.sub.4 +R.sub.5)) times when the control voltage applied to the reference filter portion 10 from the control circuit 11 is in the middle of the control range, that is, when the output voltage V.sub.1 of the operational amplifier 7 is equal to the constant voltage V.sub.3. The operational amplifier 7 is set so that the output voltage V.sub.1 equals the constant voltage V.sub.3 when positive and negative phase input voltages are equal.
Above-mentioned setting enables the operational amplifier 7 to receive equal voltages (S5, S6) when the signals (S10, S45) of the same amplitude are applied to the amplitude detectors 5, 6. The result is V.sub.1 =V.sub.3, and the damping factor of the reference filter portion 10 is kept to (R.sub.5 /(R.sub.4 +R.sub.5)), whereby the amplitude of the signal S45 damped by the resistors R.sub.4 and R.sub.5 equals that of the filtered output signal S10 of the reference filter portion 10. In this manner, a feedback loop is formed between the reference filter portion 10 and the control circuit 11. A cut-off frequency f.sub.10 of the reference filter portion 10 is expressed by Expression (18) in the same manner as Expression (17). ##EQU10##
If the element values of resistances and capacitances vary depending on variations in values of elements when fabricated, an attenuator including resistors R.sub.4 and R.sub.5 has a constant resistance ratio and, accordingly, the damping factor is not changed, but the input-output characteristic of the reference filter portion 10 varies. For example, when the cut-off frequency f.sub.10 decreases, the amount of attenuation by the filter increases and the output voltage S5 of the amplitude detector 5 decreases.
As a result, the output voltage V.sub.1 of the operational amplifier 7 increases. Thus the cut-off frequency f.sub.10 increases from Expression (18) to provide negative feedback. At this time, since the operational amplifier 7 has a sufficiently large gain, the control circuit 11 operates to compensate for any slight variations in the amount of attenuation by the filter. The amount of attenuation is thus kept constant at all times. Since the filter portion 8 and the control portion 9 are equivalent to the reference filter portion 10 and the control circuit 11 as above discussed, the control portion 9 performs similar control on the filter portion 8.
A desired value of the input-output characteristic of the filter portion 8 is provided by selecting the values of the resistor R.sub.1 and capacitor C.sub.1. The output voltage V.sub.1 applied to the control circuit 9 is common to the control circuit 11, and controls the characteristic variations when the individual element values of the filter portion 8 vary. Accordingly, the cut-off frequency of the filter portion 8 is determined by ##EQU11##
Assuming that R.sub.1 =a R.sub.3, C.sub.1 =b C.sub.2, Expression (19) is changed into ##EQU12##
Symbols such as I and R are asterisked at upper fight to indicates that the element values have varied (except the constant voltages such as V.sub.2 and V.sub.3 because they are easily designed not to vary). The cut-off frequency f.sub.8 of the filter portion 8 when varied is expressed by ##EQU13## where ##EQU14##
The reference filter portion 10 has a characteristic kept constant at all times by automatic change of the output voltage V.sub.1 of the operational amplifier 7 if the individual element values vary. Then Expression (23) holds. EQU f.sub.10 *=f.sub.10
Expression (24) is derived from Expression (21). ##EQU15##
From Expression (24), it is found that when V.sub.2 =V.sub.3 the cut-off frequency f.sub.8 of the filter portion 8 is (1/ab).multidot.f.sub.10 which is constant at all times and is not influenced by variations in the element values in the filter portion 8. However, when V.sub.2 .noteq.V.sub.3, the following inequality is derived from comparison between Expressions (20) and (24). EQU C.sub.2 *I.sub.2 *R.sub.2 *R.sub.3 *.noteq.C.sub.2 I.sub.2 R.sub.2 R.sub.3( 25)
Accordingly, the conclusion is f.sub.8 .noteq.f.sub.8 *. It is easy to design semiconductor integrated circuits so that current values such as I.sub.2, I.sub.3 are inversely proportional to the resistances such as R.sub.2, R.sub.3, and accordingly Expression (26) holds. EQU I.sub.2 *R.sub.2 *=I.sub.2 R.sub.2 ( 26)
Expression (25) is then simplified as EQU C.sub.2 *R.sub.3 *.noteq.C.sub.2 R.sub.3 ( 27)
However, the capacitances and resistances vary independently of each other, resulting in f.sub.8 .noteq.f.sub.8 *.
The conventional filter circuit with automatic regulating function as above designed presents no problems when V.sub.2 =V.sub.3 but has been disadvantageous in that, when V.sub.2 .noteq.V.sub.3, variations in element values cause variations in input-output characteristic thereof if it is desired to obtain some characteristics by some changes of the value of V.sub.2 in a single filter circuit.